Dragon Quest 5: Flying Castle. Yes, you get to pilot a flying castle, complete with its inhabitants.
SaGa 2 (GB): Dragon. If you teleport while riding the dragon, you can escape the dragon race with it and fly it elsewhere, and it turns out that it can fly right through walls and everything else. Needless to say, this allows you to skip a good portion of the game, and it also exposes the fact that multiple shop types are stored on the same map.
SaGa 3: The Talon is one of the earliest upgradable transport vehicles in a cRPG. It is also capable of traveling through time, and assisting the party during battle. (One complaint: In the original version, once you use it to travel to the alternate dimension, you can never go back. The DS version fixed this, but you are still stuck there for a while.)